Description Usage Arguments Details Value References Examples

Estimate graphical models with latent variables and replicates using the method in Tan et al. (2016).

1 | ```
semilatent(data, n, R, p, lambda, distribution = "Gaussian", rule = "AND")
``` |

`data` |
data set. Can be a matrix, list, array, or data frame. If the data set is a matrix, it should have |

`n` |
the number of observations. |

`R` |
the number of replicates for each observation. |

`p` |
the number of observed variables. |

`lambda` |
tuning parameter that encourages estimated graph to be sparse. |

`distribution` |
For a data set with Gaussian distribution, use "Gaussian"; For a data set with Ising distribution, use "Ising". Default is "Gaussian". |

`rule` |
rules to combine matrices that encode the conditional dependence relationships between sets of two observed variables. Options are "AND" and "OR". Default is "AND". |

The semilatent method has two assumptions. The first one states that the latent variables are constant across replicates.
Assumption 2 states that given the latent variables, the replicates are mutually independent.
With these two assumptions, the method seeks to solve the following problem for *1 ≤ j ≤ p*.

*
\min_{β_{j,O / j}} \{l_j (β_{j,O / j}) + λ\|β_{j,O / j}\|_1 \},
*

where *l_j (β_{j,O / j}) * is a nuisance-free loss function, *β_{j,O / j}* is a parameter that represents the conditional dependence relationships between *j*th observed variable and the other observed variables, and *λ* is a tuning parameter.
This method aims at modeling semiparametric exponential family graphical model with latent variables and replicates.

`omega` |
a matrix that encodes the conditional dependence relationships between sets of two observed variables |

`theta` |
the adjacency matrix with 0 and 1 encoding conditional independence and dependence between sets of two observed variables, respectively |

`penalty` |
the penalty value |

Tan, K. M., Ning, Y., Witten, D. M. & Liu, H. (2016), ‘Replicates in high dimensions, with applications to latent variable graphical models’, Biometrika 103(4), 761–777.

1 2 3 4 5 6 7 8 9 10 11 12 | ```
#semilatent Gaussian with "AND" rule
n <- 50
R <- 20
p <- 30
seed <- 1
l <- 2
s <- 2
data <- generate_Gaussian(n, R, p, l, s, sparsityA = 0.95, sparsityobserved = 0.9,
sparsitylatent = 0.2, lwb = 0.3, upb = 0.3, seed)$X
result <- semilatent(data, n, R, p, lambda = 0.1,distribution = "Gaussian",
rule = "AND")
``` |

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